An equation relating a [[Linear Combination]] of a [[Ordered Set]] of [[Vector|Vectors]] equal to the [[Zero Vector]]. $\huge \begin{align} \huge \let \vec{v_{1}},\dots,\vec{v_{m}}& \in \R^{n} \\ \end{align}$ $\huge x_{1}\vec{v_{1}} + \dots +x_{m}\vec {v_{m}}=\vec b \sim \augmented{c|c}{ \vec{v_{1} } \cdots \vec{v_{m}} & \vec 0 }$ $\huge\sim A\vec x = \vec 0$ This type of equation is *never* [[Inconsistent]] as there is always a [[Trivial Solution]] where for all $x_{i}=0$, as then the sum will [[Tautology|always]] be $\vec 0$. The number of solutions will always either be $1$ or [[Infinity|Infinite]].